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Simplifying (10x2 + -7x + -2) + -1(3x2 + -4x + 6) = 0 Reorder the terms: (-2 + -7x + 10x2) + -1(3x2 + -4x + 6) = 0 Remove parenthesis around (-2 + -7x + 10x2) -2 + -7x + 10x2 + -1(3x2 + -4x + 6) = 0 Reorder the terms: -2 + -7x + 10x2 + -1(6 + -4x + 3x2) = 0 -2 + -7x + 10x2 + (6 * -1 + -4x * -1 + 3x2 * -1) = 0 -2 + -7x + 10x2 + (-6 + 4x + -3x2) = 0 Reorder the terms: -2 + -6 + -7x + 4x + 10x2 + -3x2 = 0 Combine like terms: -2 + -6 = -8 -8 + -7x + 4x + 10x2 + -3x2 = 0 Combine like terms: -7x + 4x = -3x -8 + -3x + 10x2 + -3x2 = 0 Combine like terms: 10x2 + -3x2 = 7x2 -8 + -3x + 7x2 = 0 Solving -8 + -3x + 7x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. -1.142857143 + -0.4285714286x + x2 = 0 Move the constant term to the right: Add '1.142857143' to each side of the equation. -1.142857143 + -0.4285714286x + 1.142857143 + x2 = 0 + 1.142857143 Reorder the terms: -1.142857143 + 1.142857143 + -0.4285714286x + x2 = 0 + 1.142857143 Combine like terms: -1.142857143 + 1.142857143 = 0.000000000 0.000000000 + -0.4285714286x + x2 = 0 + 1.142857143 -0.4285714286x + x2 = 0 + 1.142857143 Combine like terms: 0 + 1.142857143 = 1.142857143 -0.4285714286x + x2 = 1.142857143 The x term is -0.4285714286x. Take half its coefficient (-0.2142857143). Square it (0.04591836735) and add it to both sides. Add '0.04591836735' to each side of the equation. -0.4285714286x + 0.04591836735 + x2 = 1.142857143 + 0.04591836735 Reorder the terms: 0.04591836735 + -0.4285714286x + x2 = 1.142857143 + 0.04591836735 Combine like terms: 1.142857143 + 0.04591836735 = 1.18877551035 0.04591836735 + -0.4285714286x + x2 = 1.18877551035 Factor a perfect square on the left side: (x + -0.2142857143)(x + -0.2142857143) = 1.18877551035 Calculate the square root of the right side: 1.090309823 Break this problem into two subproblems by setting (x + -0.2142857143) equal to 1.090309823 and -1.090309823.Subproblem 1
x + -0.2142857143 = 1.090309823 Simplifying x + -0.2142857143 = 1.090309823 Reorder the terms: -0.2142857143 + x = 1.090309823 Solving -0.2142857143 + x = 1.090309823 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.2142857143' to each side of the equation. -0.2142857143 + 0.2142857143 + x = 1.090309823 + 0.2142857143 Combine like terms: -0.2142857143 + 0.2142857143 = 0.0000000000 0.0000000000 + x = 1.090309823 + 0.2142857143 x = 1.090309823 + 0.2142857143 Combine like terms: 1.090309823 + 0.2142857143 = 1.3045955373 x = 1.3045955373 Simplifying x = 1.3045955373Subproblem 2
x + -0.2142857143 = -1.090309823 Simplifying x + -0.2142857143 = -1.090309823 Reorder the terms: -0.2142857143 + x = -1.090309823 Solving -0.2142857143 + x = -1.090309823 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.2142857143' to each side of the equation. -0.2142857143 + 0.2142857143 + x = -1.090309823 + 0.2142857143 Combine like terms: -0.2142857143 + 0.2142857143 = 0.0000000000 0.0000000000 + x = -1.090309823 + 0.2142857143 x = -1.090309823 + 0.2142857143 Combine like terms: -1.090309823 + 0.2142857143 = -0.8760241087 x = -0.8760241087 Simplifying x = -0.8760241087Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.3045955373, -0.8760241087}
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